Exhibit 5.1

January 15, 2020

Gardner Denver Holdings, Inc.

222 East Erie Street, Suite 500

Milwaukee, Wisconsin 53202

Ladies and Gentlemen:

We have acted as counsel to Gardner Denver Holdings, Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-4 (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended, relating to the issuance by the Company of up to 213,000,000 shares of Common Stock, par value $0.01 per share (the “Shares”), in connection with the merger contemplated by the Agreement and Plan of Merger, dated as of April 30, 2019 (the “Merger Agreement”), by and among the Company, Ingersoll-Rand plc, a Republic of Ireland public limited company, Ingersoll-Rand U.S. HoldCo, Inc., a Delaware corporation and newly formed wholly-owned indirect subsidiary of Ingersoll-Rand plc, and Charm Merger Sub Inc., a Delaware corporation and newly formed, wholly-owned subsidiary of the Company.

Simpson Thacher & Bartlett LLP	January 15, 2020
Gardner Denver Holdings, Inc.

We have examined the Registration Statement, the Merger Agreement and a form of the share certificate relating to the Shares, which has been filed with the Commission as an exhibit to the Registration Statement.  In addition, we have examined, and have relied as to matters of fact upon, originals, or duplicates or certified or conformed copies, of such records, agreements, documents and other instruments and such certificates or comparable documents of public officials and of officers and representatives of the Company and have made such other investigations as we have deemed relevant and necessary in connection with the opinions hereinafter set forth.

In rendering the opinion set forth below, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as duplicates or certified or conformed copies and the authenticity of the originals of such latter documents.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that, when issued in accordance with the terms and conditions set forth in the Merger Agreement, the Shares will be validly issued, fully paid and nonassessable.

We do not express any opinion herein concerning any law other than the Delaware General Corporation Law.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement and to the use of our name under the caption “Legal Matters” in the proxy statement/prospectus-information statement included in the Registration Statement.

Very truly yours,

/s/ Simpson Thacher & Barlett LLP

SIMPSON THACHER & BARTLETT LLP